Question

While light is used to illuminate the two slits in Young's double slit experiment. The separation between the slits is d and the distance between the screen and the slit is D (>> d). At a point on the screen directly in front of one of the slits, certain wavelengths are missing. The missing wavelengths are (here m=0, 1, 2, .....is an integer)

• A. $\frac{d^2}{(2m+1)D}$
  
• B. $\frac{(2m+1)d^2}{D}$
  
• C. $\frac{d^2}{(m+1)D}$
  
• D. $\frac{(m+1)d^2}{D}$

Answer 1

The correct option is A

$\frac{d^2}{(2m+1)D}$

The distance of the mth minimum from the centre of the screen is given by
$y=(m+\frac{1}{2})\frac{\lambda D}{d}$
For a point on the screen directly in front of one of the slits, y=d/2. Hence, for minima (zeros) of intensity, we have
$\frac{d}{2}=(m+\frac{1}{2})\frac{\lambda D}{d}or\lambda =\frac{d^2}{(2m+1)D}$